Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Lin, Quyuan"'
Autor:
Abdo, Elie, Lin, Quyuan
We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincar\'e inequalities. We also use these tools to study the long-time dynamics of the surface qua
Externí odkaz:
http://arxiv.org/abs/2409.05209
The deterministic inviscid primitive equations (also called the hydrostatic Euler equations) are known to be ill-posed in Sobolev spaces and in Gevrey classes of order strictly greater than 1, and some of their analytic solutions exist only locally i
Externí odkaz:
http://arxiv.org/abs/2407.21336
We consider coarsening dynamics associated with a Burgers--Cahn--Hilliard system modeling a two-phase flow in one space dimension. Our emphasis is on the effect that coupling between the phase and fluid dynamics has on coarsening rates, and on the me
Externí odkaz:
http://arxiv.org/abs/2405.11709
In this paper, we analyze a three-dimensional Nernst-Planck-Boussinesq (NPB) system that describes ionic electrodiffusion in an incompressible viscous fluid. This new model incorporates variational temperature and is forced by buoyancy force stemming
Externí odkaz:
http://arxiv.org/abs/2405.02152
In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise. By assuming the ionic species have the same diffusivity and opposite valences, we prove the global well-posedness of the system. Furthermore, we
Externí odkaz:
http://arxiv.org/abs/2401.11318
We systematically analyze the accuracy of Physics-Informed Neural Networks (PINNs) in approximating solutions to the critical Surface Quasi-Geostrophic (SQG) equation on two-dimensional periodic boxes. The critical SQG equation involves advection and
Externí odkaz:
http://arxiv.org/abs/2401.10879
We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear drift-diffusi
Externí odkaz:
http://arxiv.org/abs/2310.20484
The viscosity parameters plays a fundamental role in applications involving stochastic primitive equations (SPE), such as accurate weather predictions, climate modeling, and ocean current simulations. In this paper, we develop several novel estimator
Externí odkaz:
http://arxiv.org/abs/2309.06952
In this paper, we consider the stochastic Boussinesq equations on $\mathbb T^3$ with transport noise and rough initial data. We first prove the existence and uniqueness of the local pathwise solution with initial data in $L^p(\Omega;L^p)$ for $p>5$.
Externí odkaz:
http://arxiv.org/abs/2303.09768
Autor:
Hu, Ruimeng, Lin, Quyuan
Stochastic factors are not negligible in applications of hydrostatic Euler equations (EE) and hydrostatic Navier-Stokes equations (NSE). Compared with the deterministic cases for which the ill-posedness of these models in the Sobolev spaces can be ov
Externí odkaz:
http://arxiv.org/abs/2301.07810